(4x-23)(3x+16)=180

Solution for (4x-23)(3x+16)=180 equation:

(4x-23)(3x+16)=180

We move all terms to the left:

(4x-23)(3x+16)-(180)=0

We multiply parentheses ..

(+12x^2+64x-69x-368)-180=0

We get rid of parentheses

12x^2+64x-69x-368-180=0

We add all the numbers together, and all the variables

12x^2-5x-548=0

a = 12; b = -5; c = -548;
Δ = b2-4ac
Δ = -52-4·12·(-548)
Δ = 26329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{26329}}{2*12}=\frac{5-\sqrt{26329}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{26329}}{2*12}=\frac{5+\sqrt{26329}}{24}
$